A Phantom does not Result from a Backreaction

Abstract

The backreaction of nonlinear inhomogeneities to the cosmic expansion is analyzed in the framework of general relativity with a cosmological constant. By defining the spatially averaged matter energy density, we find that the cosmological constant induces a new type of backreaction whose equation of state is $p=-4/3 ρ$, where $ρ$ and $p$ are the effective energy density and effective pressure of the backreaction in the averaged Friedmann universe. However, the effective density is negative, and thus it decreases the acceleration caused by the cosmological constant.